Solving Quadratic Equationsby Completingthe Square - Example 4
The Discriminant - Example 4
Liberty University
Solve Quadratic Equationsby Graphing - Example 4


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the quadratic equation X squared plus X plus 20 equal zero biographic. So the first thing I'm gonna look for my graph is I'm gonna go ahead and try to find my y intercept. Well, there, I'm gonna be looking for my constant and my Y intercept is 20. So that means that when x zero my wife is going to be 20. Well, I don't have room on my graph for that one, so we're not gonna use that point, But we are going to go ahead and find the axis of symmetry. The axis of symmetry is basically the center line. That's where your Vertex is gonna hit and divide the parable in half. So let's find some points. Remember, Axis of symmetry is negative. Be over to a In this case, RB is positive one and are a is negative one. So we would have negative one over negative too, which would be positive one half. So that means that my axes of symmetry is going to be between zero and one. Now we already know what zero is, and there's a good chance because one is on the other side is also going to be 20 So let's kind of go from there and less kind of spread out some. So let's move down. Let's just kind of do some even number. So let's do mm. We'll do positive to and negative two. We'll try those two numbers and we'll see what we get, and then we can adjust from that point. So for positive, two would have negative two squared plus two plus 20. So that's going to give me a negative four plus two plus 20. And so that's going to give me a positive 80. Well, that's a little bit larger than my graph, but that's okay, just kind of keep. That's not what we're looking for you to remember. We're trying to get where why is gonna be zero. So let's do. Let's do negative, too. So be negative. Negative two squared minus to plus 20. So that would be negative. Four minus to plus 20. And that's going to give May 14. Well, that's a little bit better, but that's still it's pretty far away, so let's go spread out a little bit more. Let's go. Uh huh. Let's try four and may be negative for Let's see what those two points give me Sometimes there's a little bit of a trial and error, so let's do four. So we'd have negative for squared plus four plus 20. So that would be negative. 16 plus four plus twitting and that's gonna be positive. Eight. Well, that's a little bit better. So let's kind of let's start with there. So So we're getting them on the graph. So there's positive. Eight. So let's try. Negative four to be negative. Negative four squared minus four plus 20. So that would be negative. 16. Minus four plus 20. And that's going to equal +00 there's the number we like, so that would be zero. So somewhere we need to get and remind you, this is a This is a negative. Remember, this parable is going in a downward direction. OK, so somewhere we need to get this point, um, to start coming down. So let's spread out a little bit. Mawr. So let's try positive five. So let's do negative five squared plus five plus 20. So that would be a negative 25 plus five plus 20 and that would equal zero. So basically what we're saying is our parabola would be kind of like this and it would come off and it would be kind of like this. So this would be one really high one or with very high minimum and maximum, and it would continue on down that way. So But I do see my two solutions because we're really just seeing where it crosses that X axis here and here. Even if we can't see our whole Graf those were the two points we're looking for, where X is negative four and X is positive. So our solution, It's negative. Four positive bath.